Does it make difference if you paint a wall black or white?

If yes, how does it work?

• How does painting a wall have any relation to blackbody radiation? An incandescent light bulb is an application of black body radiation. Jun 4, 2014 at 4:49
• How does it make a difference to what?
– BMS
Jun 4, 2014 at 4:59
• @Larara : Hi, I am guessing that you want to know about the application of the black body radiation theory to a (house) wall, yes? Perhaps you can add a little more detail of exactly what it is that is bothering you. Also, note that when we say "Black Body" we do not exactly mean something that is the colour black. It is a definition for something which emits electromagnetic radiation at all wavelengths (or equivalently frequencies) with a characteristic spectrum. No body (except maybe the Cosmic Microwave Background, anyone?) is truly 'black' in this sense (again, corrections welcome?). Jun 4, 2014 at 6:32
• For all, sorry for the unclear question, and thanks for reading! Next time, I'll be more detailed. Jun 5, 2014 at 13:00

Since this is your first question and you are new here, I will answer what I think you are saying. The negative votes are because you are not clear in your question.

Does it make difference if you paint a wall black or white?

If yes, how does it work?

Yes, it makes a difference to the temperature in the room inside. Black absorbs the visible light (and usually the ultraviolet and infrared too), that is why we see it black. The energy turns into heat into the wall, the temperature of the wall gets higher and the room is heated.

White reflects most of the light so the effect of temperature increase in the walls and in the room is much smaller.

Now if you want to compute the temperatures and temperature differences you would have to use the black body radiation formulae, on how the heating of the wall radiates infrared into the room and raises its temperature.

Further to Anna's answer: the energy radiated by a body at a temperature $T$ is given by the Stefan-Boltzmann law:

$$J = \epsilon\sigma T^4$$

where $\sigma$ is the Stefan-Boltzmann constant and $\epsilon$ is the emissivity. A black body has an emissivity of one, but real materials always have an emissivity of less than one, and sometimes much less than one.

When you paint the walls of your house white you are reducing the emissivity because white paint has a lower emissivity than black paint. This means that the wall will both emit less radiation and absorb less radiation.

The reason for painting walls white is that walls generally heat up by absorbing radiation from the Sun, but they generally lose the heat by heating the air next to them (this is called convection). The rate of heat loss in convection is not affected by the emissivity, but the rate of heat gain is decreased if the emissivity is decreased. The end result is that white walls stay cooler than black ones.